This class of singular integrals is of interest in Harmonic analysis. It was well-known that \(T_{\Omega ,\,A}\)  is closely related to the study of Calderón commutators [1]}, [2]}.
Even for smooth kernel \(\Omega \) , since \({L^\infty (\mathbb {R}^d)}\subset {\rm BMO}(\mathbb {R}^d)\) , the kernel of the operator \(T_{\Omega ,\,A}\)  may fail to satisfy the classical standard kernel conditions. This is the main reason why one calls them nonstandard singular integral operators.
